View source for User:Dominus/Sandbox

==Backup of MJD article==

[[User:Dominus/Sandbox/MJD]]

==Other stuff==

{{cite journal | journal = [[Science (journal){{!}}]] | title = Article | last1 = Flooney | first1 = Fred | volume = 3 | issue = 17 }}

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==Stuff==

''A Discourse Concerning the Beauty of Providence'' (1649) took an unfashionable line, namely that [[divine providence]] was more inscrutable than current interpreters were saying. It added to the reputation of Wilkins, when the Stuarts returned to the throne, to have warned that the short term reading of events as managed by God was risky.<ref>{{cite book | title = Providence and the Invention of the United States, 1607-1876 | last1 = Guyatt | first1 = Nicholas | publisher = [[Cambridge University Press]] | year = 2007 | page = 43 | isbn = 9780521867887 }}  Guyatt quotes Wilkins as saying "Bo do de do".</ref>
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{{#expr: pi}}

{{Userboxtop}}
{{User Wikipedian For|year=2002|month=11|day=23}}
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{{harvtxt|Mac Lane|1998}}

{{Citation | last1=Mac Lane | first1=Saunders | author1-link=Saunders Mac Lane | title=[[Categories for the Working Mathematician]] | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-0-387-98403-2 | year=1998}}


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<references/>


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<math>
       { \Gamma \vdash \alpha  \qquad  \Sigma, \beta  \vdash \gamma \over
          \Gamma, \Sigma, \alpha\rarr\beta  \vdash\gamma} \qquad  ({\rm Left} \rarr)
</math>

(Left &rarr;)
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<math>\input prooftree</math>

-----

                        B|-b          a|-a
                        ------------------ Left \rarr ('G = b, 'S = {})
        g |- g             b,b\rarr a |- a
        ----------------------------------- Left \rarr ('G = g, S = b\rarr a)
                g,b\rarr a,g\rarr b |- a
                ----------------- Right \rarr 
                b\rarr a,g\rarr b |- g\rarr a
                ---------------------- Right \rarr
                b\rarr a |- (g\rarr b) \rarr g\rarr a
                --------------------------- Right \rarr
                |- (b\rarr a) \rarr (g\rarr b) \rarr g\rarr a


<math>

{{
{ 
  {\gamma\vdash \gamma \qquad
    {{\beta\vdash \beta \qquad \alpha\vdash \alpha} \over {\beta,\, \beta\rarr \alpha \vdash \alpha}} Left \rarr (\Gamma = \beta,\, \Sigma = \emptyset)}
  \over
  {\gamma,\, \beta\rarr \alpha,\, \gamma\rarr \beta \vdash \alpha}
} Left \rarr (\Gamma = \gamma,\, \Sigma = \beta\rarr \alpha)
} \over
{ \beta\rarr\alpha,\, \gamma\rarr\beta\vdash\gamma\rarr\alpha}}
Right \rarr

</math>

—[[User:Dominus|Dominus]] 17:01, 4 November 2008 (UTC)
—[[User:Dominus|Dominus]] ([[User talk:Dominus|talk]]) 15:15, 15 December 2008 (UTC)